﻿ 具有四个素因子的奇亏完全数 On Odd Deficient-Perfect Numbers with Four Distinct Prime Divisors

Pure Mathematics
Vol.06 No.05(2016), Article ID:18558,7 pages
10.12677/PM.2016.65056

On Odd Deficient-Perfect Numbers with Four Distinct Prime Divisors

Lan Cui, Cong Zhang, Ying Li

Department of Mathematics and Finance, ABa Teachers University, Wenchuan Sichuan

Received: Sep. 1st, 2016; accepted: Sep. 15th, 2016; published: Sep. 20th, 2016

ABSTRACT

For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n, we call n a deficient-perfect number if. On the basis of the references, we characterize some properties of odd deficient-perfect numbers with four distinct prime divisors. We prove that if is an odd deficient-perfect number, then p1 = 3, p2 ≤ 13, and improve the result of the references.

Keywords:Deficient-Perfect Numbers, The Sum of the Positive Divisors, Prime Factors, Order

1. 引言与主要结果

， (1)

2. 一些引理

。 (2)

(3)

(4)

(5)

。 (6)

3. 主要结果的证明

，矛盾，因此。同理，由于，则

，且时，当，且时，分别计算的值如下：

，以及时，，与(5)式均为矛盾。

On Odd Deficient-Perfect Numbers with Four Distinct Prime Divisors[J]. 理论数学, 2016, 06(05): 411-417. http://dx.doi.org/10.12677/PM.2016.65056

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